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Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities

Contents

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities

Algebraic Identities Exercise 12A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Use direct method to evaluate the following products :
(i) (x + 8)(x + 3)
(ii) (y + 5)(y – 3)
(iii) (a – 8)(a + 2)
(iv) (b – 3)(b – 5)
(v) (3x – 2y)(2x + y)
(vi) (5a + 16)(3a – 7)
(vii) (8 – b) (3 + b)
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 2

Question 2.
Use direct method to evaluate :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 3
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 4

Question 3.
Evaluate :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 5

Question 4.
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
(i) 21 × 19
(ii) 33 × 27
(iii) 103 × 97
(iv) 9.8 × 10.2
(v) 7.7 × 8.3
(vi) 4.6 × 5.4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 6

Question 5.
Evaluate :
(i) (6 – xy) (6 + xy)
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 7
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 8
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12A 9

Algebraic Identities Exercise 12B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Expand :
(i) (2a + b)2
(ii) (a – 2b)2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 10
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 11

Question 2.
Find the square of :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 12
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 13
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 14

Question 3.
Evaluate:
Using expansion of (a + b)2 or (a – b)2
(i) (208)2
(ii) (92)2
(iii)(415)2
(iv) (188)2
(v) (9.4)2
(vi) (20.7)2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 15

Question 4.
Expand :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 16
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 17

Question 5.
Find the cube of :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 18
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12B 19

Algebraic Identities Exercise 12C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
If a  +b = 5 and ab = 6; find a2 + b2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 20

Question 2.
If a – b = 6 and ab = 16; find a2 + b2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 21

Question 3.
If a2 + b2 = 29 and ab = 10 ; find :
(i) a + b
(ii) a – b
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 22

Question 4.
If a2 + b2 = 10 and ab = 3; find :
(i) a – b
(ii) a + b
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 23

Question 5.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 24
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 25

Question 6.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 26
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 27

Question 7.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 28

Question 8.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q8
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 29

Question 9.
If a + b + c = 10 and a2 + b2 + c2 = 38; find ab + bc + ca
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 30

Question 10.
Find a2 + b2 + c2 ; if a + b + c = 9 and ab + bc + ca = 24
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 31

Question 11.
Find a + b + c; if a2 + b2 + c2 = 83 and ab + bc + ca = 71
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 32

Question 12.
If a + b = 6 and ab=8; find a3 + b3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 33

Question 13.
If a – b = 3 and ab = 10; find a3 – b3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 34

Question 14.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q14
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 35

Question 15.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q15
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 36

Question 16.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q16
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 37
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 38

Question 17.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C Q17
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 39
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 40

Question 18.
The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12C 41

Algebraic Identities Exercise 12D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 42
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 43

Question 2.
Evaluate:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 44
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 45
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 46

Question 3.
Find the square of :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 47
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 48

Question 4.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 49

Question 5.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 50

Question 6.
If a2 + b2 = 41 and ab = 4, find :
(i) a – b
(ii) a + b
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 51

Question 7.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 52

Question 8.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D Q8
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 53

Question 9.
Expand :
(i) (3x – 4y + 5z)2
(ii) (2a – 5b – 4c)2
(iii) (5x + 3y)3
(iv) (6a – 7b)3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 54

Question 10.
If a + b + c = 9 and ab + bc + ca = 15, find: a2 + b2 + c2.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 55

Question 11.
If a + b + c = 11 and a2 + b2 + c2 = 81, find ab + bc + ca.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 56

Question 12.
If 3x – 4y = 5 and xy = 3, find : 27x3 – 64y3.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 57

Question 13.
If a + b = 8 and ab = 15, find : a3 + b3.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 58

Question 14.
If 3x + 2y = 9 and xy = 3, find : 27x3 + 8y3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 59

Question 15.
If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 60

Question 16.
The difference between two numbers is 5 and their products is 14. Find the difference between their cubes.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 12 Algebraic Identities Ex 12D 61

Selina Concise Mathematics Class 8 ICSE Solutions

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